Parallel dynamics of continuous Hopfield model revisited

TL;DR

This paper applies generating functional analysis to the continuous Hopfield model, confirming its predictions align well with simulations and connecting it to other analytical methods, thus enhancing understanding of its dynamics.

Contribution

The study introduces the application of generating functional analysis to the continuous Hopfield model and compares its predictions with simulations and existing methods.

Findings

GFA predictions match simulation results in typical cases.

Omitting retarded self-interaction simplifies GFA to known methods.

Connections established between continuous and binary Hopfield models.

Abstract

We have applied the generating functional analysis (GFA) to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded self-interaction term is omitted, the GFA result becomes identical to that obtained using the statistical neurodynamics as well as the case of the sequential binary Hopfield model.